Equitable Partition

Equitable partition aims to divide a network or dataset into subsets with similar internal structures or properties, a crucial task in various fields. Current research focuses on developing efficient algorithms, such as those based on approximate equitable partitions, optimal transport, and semidefinite programming, to address challenges posed by large datasets and imbalanced partitions. These advancements improve the accuracy and scalability of partitioning methods, particularly for applications like graph embedding, clustering, and network analysis. The resulting improvements in data analysis and network understanding have significant implications for diverse fields ranging from machine learning to social network analysis.